Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <iostream>
#include <algorithm>
#include <cstdio>
using namespace std;
int main(void){
    int n;
    double ans=0;
    cin>>n;
    double a[n];
    for(int i=0;i<n;i++){
        cin>>a[i];
    }
    sort(a,a+n,greater<int>());
    for(int i=0;i<n-1;i++){
        for(int j=i+1;j<n;j++){
            double s=a[i]-a[j];
            double b=0;
            if(i>1)b=a[0]+a[1];
            else if(i==1){
                b+=a[0];
                if(j==2)b+=a[3];
                else b+=a[2];
            }else{
                if(j==1)b=a[2]+a[3];
                else if(j==2)b=a[1]+a[3];
                else b=a[1]+a[2];
            }
            ans=max(ans,b/s);
        }
    }
    printf("%.6lf\n",ans);
}